Reference Sliding Variable Based Discrete-Time Sliding Mode Control

The study considers the problem of sliding mode controller design for sampled-data systems with disturbances. We propose a new discrete-time switching type control scheme using a predesigned evolution of the sliding variable as a reference and a trajectory following reaching law. We show that this approach ensures the existence of the quasi-sliding mode in the sense of Gao et al. Additionally, under the assumption of boundedness and smoothness of continuous-time disturbance, we complete our strategy with a disturbance compensator. It's aim is to calculate the previous disturbance value based on the current and previous state measurement, and use it to compensate for the disturbance in the current step. Finally, we prove that the application of this compensator leads to the reduction of the quasi-sliding mode band width to O(T²) order. The effectiveness of the proposed control strategy is verified with a simulation example.